A Type-theoretical Analysis of Complex Verb Generation
Satoshi Tojo Mitsubishi Research Institute, Inc. 2-22 Harumi 3, Chuo-ku Tokyo 104, Japan e-mail: [email protected], [email protected]
Abstract hardly find a verb element in the target language, which corresponds with the original word exactly in Tense and aspect, together with mood and modality, meaning. However we also need to admit that the usually form the entangled structure of a complex verb. problem of knowledge representation of tense and as- They are often hard to translate by machines, because pect (namely time), or that of mood and modality is of both syntactic and semantic differences between lan- not only the problem of verb translation, but that of guages. This problem seriously affects upon the gen- the whole natural language understanding. In this pa- eration process because those verb components in in- per, in order to realize a type calculus in syntax, we terlingua are hardly rearranged correctly in the target depart from a rather mundane subset of tense, aspects, language. We propose here a method in which each and modMities, which will be argued in section 2. verb element is defined as a mathematical function ac- cording to its type of type theory. This formalism gives 1.2 The difference in the structure each element its legal position in the complex verb in the target language and certifies so-called partial trans- In the Japanese translation of (1): lation. In addition, the generation algorithm is totally oyoi-de-i-ta-rashii free from the stepwise calculation, and is available on parallel architecture. the syntactic main verb does not change from oyoi- (swim), which is the original meaning carrier; and the past tense is replaced by -ta- which is indistinguishable 1 The problem of complex between past and perfect in Japanese. The feature of verb translation English verb complex derivation is the alternation of the syntactic main verb, described in fig. 1. On the 1.1 The difference between languages (~ (b~ (swim))) +-- 'seem' In this section, we will briefly mention the difficulties past progressive of complex verb translation. The term complex verb refers to those verb structures that are formed with (seem (to ~ (~ (swim)))) modal 'verbs and other auxiliary verbs in order to ex- past progrcssive press rnodMity or aspects, and which are attached to Figure 1: new verb arrival in English the original base verb. For example, in a complex verb: contrary in Japanese, new verb elements are aggluti- seems to have been swimming (1) nated at the tail of verbs, as is shown in fig. 2. (,~U,))) 'swim' is in both the progressive aspect and the past (~ ( ~-dei- ~-- 'rashii(seem)' tense, upon which 'seem' is attached with the inflec- swim progressive past tion of agreement for the third person singular. Such a structure is so often hard to translate to other lan- guages both because surface structures become dif- swim pro9 resslve past ferent between languages, and because some aspec- Figure 2: new verb arrival in Japanese tual/modal concepts cannot be found in the target lan- guage in the generation process. 1 We admit that the most recalcitrant problem in verb 1.3 The existence of external modal- phrase translation is that the differences of tense, as- pect, mood, and modality systems. Hence, we can ities XThe systems of tense, aspect, and modality are different In the history of machine translation, the analysis of a from language to language, and their typology ha.s been dis- complex verb structure seems to have been rather ne- cussed in linguistics [1], [21, [9]. glected. Even in an advanced machine translation sys-
1 353 tem of CMU-CMT [8], a verb complex is represented Externality To clarify the externality of modal conventionally like: functions mentioned in the previous section, we put the following definition: (vp (root . ..) (negation +/-) Definition of externality: We call those (modality .... ) modal functions which can have their own (tense .... ) tense and negation external; otherwise we call (aspect ...) ) them internal. However this flat description fails in the following cases. Interlingua Here we propose the simplified sets of First, certain modalities can have their own nega- modalities, aspects, and tenses, which are recognizable tion. The sentence both in English and in Japanese, mostly based upon the work of [7]. You must play. ( [:l[you play])
can be negated in two ways: tense = {past, present, future} aspect = {progressive, perfect, iterative, in- You must not play. choative, terminative} ([:3--[you play] = [:3[you don't play]) external modality You don't have to play. = {possible, necessaw}®{epistemic, deontic} (-~D[you play S or {hearsay, seem} internal modality = {able} The former is the negation of 'must' while the latter is the negation of the sentence, where in parentheses The two dimensional analysis of eplstemic and deontic above [] is necessity and -~ is negation operator. is considered, reflecting the duality in meaning of 'may' A similar thing can be said for tense. A certain kind and 'must'. of complex verbs such as 'seem to be' can have two positions to be tensed as below: Verb elements as function We assume that the crude result of a parsing process for a complex verb is seemed to have been the list of verb elements such as:
It has been discussed that there are so called ex- ternal modal expressions, that are embedded from the past1, seem, past2,progressive, swim,... (2) outside of the sentence ([3], [4], [10], [11], and [14]). The key issue is that those external ones concern only Our objective is: the speaker's attitude of the sentences in illocutionary situations in order to express deonticity, uncertainty, * to construct the interlingua expression from these and so on, and are indifferent to the sentence subjects. verb elements such as: Although there should be a controversial discussion as (q-ed(seem)) ((-t-ed(progres sive)) (swim)) to whether a certain modal verb is connected to speak- ers or not 2, we will engage this matter in the following • and to derive a surface structure of the target lan- formalization of complex verb translation. guage from the interlingua expression.
In order to do this, we will regard each verb element 2 Formalization of complex as a function. The main concern here is the domain of verb translation each function. For example, an external "past" oper- ator +ed should operate upon external verbs, not in- We will give a formal definition of modality as a func- cluding internal verbs. We will realize this idea, being tion here, and discuss the strategy of verb complex independent of each intra-grammar in complex verbs generation in which each modal element is used as a of various languages, in the following section. function itself. In this section we use the term 'modal We express a verb complex as a composition of a functions' both for modal operators and aspectuM op- root-word, tense, negation, and verb-complement, erators as long as there is no confusion. in which root and verb-form are included; veomp may be included recursively. 2Although the concept of modality is based on the deontic distinction/epistemic between possibility and necessity such as Fig. 3 is an example of a ,k-function of tt perfect: 'can', 'may', 'must', tbe term is sometimes used in a broader sense inclusively 'will'(volitive) or 'can'(ability). We distin- `kxVe~b-,t~c~u~e.perfeet(x) guished the externality by its independent tense and polar- ity (positive/negative), so that broad-sense modal verbs such as volitive and ability are regarded as actually internal while which takes a verb structure as a parameter, and pro- narrow-sense ones are often external. duce a more complicated structure.
354 (vp (roet; be) 3.2 A simple example (tense negation) Let us consider an example of concatenating seem with (vcomp (root swim) +ed(swim). First, assume that we can infer the type of (vform ing) )) +ed(swim) to be ~1 from F by a variable instantiation (~p O'oot h~ve) 0, as is shown below in (3): (tense negation) r0 ~ +ed(s~im): V'~ (3) (vcomp (root be) (vrorm pp) As for seem : ext, because 'ext' was a mnemonic for (vcemp (root swim) a certain modifier of a verb phrase, we can put ext = (vform ing)))) (~1 -~ 5~). Hence, for a new type variable 9a2, set r/1 as (4): Figm'e 3: perfect-ization in English ~q, = mgu(extO, W -4 p~) (4) 3 Type inference for complex verb composition Note that we have not specified the contents of 7h We will make use of polymorphic type theory [6] in the yet; we will give them later. We can now infer the fnrther formalization. The reason we adopt the type type of combined verb phrase with (4), as is shown in formalism is to realize "the internality of concatenation fig. 4 where we can use a canonical expression (see [5]) rules"; namely each verb element shonld know which Ax.seem(x) instead of seem. elements to operate upon, instead of being given a set of grammar on concatenation. Behind this purpose lie tile following two issues: ]-"/1 ~ seem: extT}l r0/]l [- +ed(swim): qCl~h (_+ E)
• parallel computation: to realize a fas~ parallel computation on coming parallel architecture F'igure 4: inference of seem(+ed(swim))
, partial translation: for machine translation to \Ve use '~' to denote that the type of the left-hand be robu:-'t for ill-founded information in the lexicon side is more instantiated than that of the right-hand side, so that: 3.1 ~pes for verb phrase
First we will set up several mnemonic types. They are not terminal symbols of type calculus, but mnemonic 3.3 Full-fledged verb type identifiers of certain types. A set of mnemonic types: In order to analyze the contents of 0 in (3) in detail, we need to clarify what tensel actually does. We will {root, int, ext, teasel, negi, tense~, ne9~} argue what each mnemonic means in this subsection. Concretely saying, we will specify what kind of internal For example, we can assume the following r' as a result variables can occur in various verb types. of our parser. Our presupposition is that a 'full-fledged' complex verb contains 'external part' as well as 'internal part'. F = {seem : ext,+ed : tensei, swim : root, So that a verb type ~, is assumed to have two internal progressive : int} type variables ~oi,,t and ~oCxt. Each of them has a 'head' verb which incurs tense or negation if exists. We call a where a : a means that a is of type a. (In that parser, compound of tense and negation 'cap'. As for a cap, each syntactic category in the source language was re- we assume a construction of: placed by a mnemonic type that is actually regarded as negation(tense(X)) a a category of the interlingua.) We use cp as a type vari- able denoting 'verb phrase , . Because we can regard any As a result, our full-fledged verb type becomes as fig. 5. verb element as a modifier from a verb phrase to an- other phrase, those mnemonic types are always unified aThis formalization is actually after the consideration of the following generation process. When we construct a past and with a type '~ -~ qo', except 'root' of type ~. The type negation of 'walk': 3 355 +ing' can join tim 'seem(+ed(swim))' structure, and neg --~ tense neg --~ tense also correctly choose the target element 'swim' from cape eapi the structure, instead of 'seem' which exists most ex- / / teriorly. 0 --,0-, O O If there is such a set of instantiation 772 that: head~ headl root external internal 712 = mgu(intOth, ~Th ~ ~3) (5) then we can validate the inference in fig. 7. However, Figure 5: complex verb structure because the domain of int must be 'cap'-less ~i,t, we cannot legalize the type inference of fig. 7 immediately. Let us get back to the type inference of +ed(swim) What we are required to do now is a type 'demo- here, to see the basis of our formalism of type unifica- tion', as opposed to the promotion. Roughly saying, tion. +ed is of type tensei, and swim is of type root a verb type of seem(+ed(swim)) is regarded as below: that was a mnemonic for simple T. 0 in (3) becomes as follows: (6) though each of the right hand side of (6) is promoted 0 = mgu(tensei,root ~ ~a) to some qualified type. This means that the history of Because tensei itself is not a function, it must be qual- promotion must be included in the unifier 0. Hence, ified as of type capl to act as a function by itself. We we can scrutinize the contents of 0 so that we may find call this qualification 'promotion', to mean that the where int can be embeddable. In this case, component raises its type to connect with others. The { r oot / headi, headl/ ~pi~t } similar thing can be said for root, which must be pro- moted to ~nt SO as to be in the domain of cap~. Fig. 6 in 0 (viz. ~i~t ~ int) should be demoted, and we can depicts the type promotion. redefine a verb type of (6) as: ten e,(root) ) --, tens ,(.d"'(root) ) ) tense; root J. J. promote Suppose that r/a replaces the history of promotions capi[¢/negl] p,~,[,'oot/head,] and demotions as below: % / capdPint) (F U {~9:i,lt})0~71r/3 F seem(+ed(swim)): ~4 .~ promote then we can make the inference in fig. 8. In this case, 4,I q~,,[root[¢ /neg, 1/tense]/ head,] promote { r U q~ : int }O,h tl3 f- seem(+ed(swim)) : ~4 , ~[¢/c2~xt, root[C/ne9, 1/ tense]/ headi] ...... ~-~ I) ['0rl,rl3 I- ~.seem(+ed(~o(swim))): int,]3 -~ ~4 Figure 6: type promotion Figure 8: inference of A-abstraction A unifier, or what we have called a set of instanti- there is only a place for int to be embedded in between ation so far, like 0 or '7 is exactly a set of promotions +ed and swim, and int operates upon a root. where some missing verb elements (compared with full- This time, we can make an inference from abstracted fledged type) are ignored or replaced by other elements. verb structure, as is shown in fig. 9. For example, the contents of 0 becomes as follows: 0 = [¢/negl, tensei/capl,root/headi, 3.5 Head shifting he d,l ,int, We mentioned that another superiority of type formal- ism is its partiality. Actually we can compose a verb 3.4 Component embedding stru'cture from any part of given interlingua set, and this feature is realized dynamically. The computation In the type inference of fig. 4, we happened to choose of verb complex generation may be stopped any time two items of seer. and +ed(suim). Actually, we can by ill-foundedness of machine translation system. Even combine any two items picked up from F. In this in such a case, our formalism can offer a part of sur- subsection we will show an example, in which we face structure which had been partially completed so try to concatenate the consequence of fig. 4 with far. The type definition above gives us an important progressive : int. In the conventional generation, an clue to how to compose verb elements. The algorithm internal verb element such as 'progressive' must be con- necessarily becomes as follows: catenated to the structure, prior to an external element such as 'seem'. However, in our type expression, 'be 1. Pick up an original meaning base. 4 356 FOr/, 1- seem(+ed(sw£m)) : ~2r/, I" I- progressive:int(__+ E) V@lr/2 b progressive( seem( +ed( swim) ) ) : ~o3r12 Figure 7: ill-founded type inference F b +ed : tensei F b swim : root FF seem:ext F0 b +ed(swim) : ~1 F I- A Figure 9: inference with A-calculus 2. Apply internal modal functions, while .. 2. Because the order of calculation is not specified in the type expression, the verb structure can be 3. Shift the internal tense and negation to a newly composed in a way of self-organization, in tile applied modal function. meaning that tile structure is able to be decom- posed and to be reorganized in the process. 4. Apply external modal functions, while .. In the case of complex verb translation, rephrasing to 5. Shift the external tense and negation to a newly another part of speech is rather easier; we only need applied modal flmction. to 'kick out' the functional expression from the verb structure to point to another lexical item. Some ex- The position shift of tense, caused by the arrival of ternal expressions must be translated into a complex a new internal verb, is diagramed in fig. 10. Fig. 11 sentence as the feature of externality, as we have dis- cussed in section 1.3. We give here a definition of the English identity in meaning between an external verb and its (Vp new-root . . (tense).. (vcomp .. e.. ) corresponding complex sentence in the type-theoreticM k______j view as (7): 5 357 of CMU-CMT and Institute for New Generation Com- puter Technology (ICOT) for many significant com- ments. References [1] B. Comrie. Aspect. Cambridge University Press, 1976. root vform vcomp [2] B. Corm'ie. Tense. Cambridge University Press, 1985. swim past +progressive [al O. Jesperson. The Philosophy of Grammar. Allen vp and Unwin, London, 1924. [4] J. Lyons. Semantics vol.1,2. Cambridge Univer- sity Press, 1977. root vform vcomp I I P. Martin-Loef. Intuitionistic Type Theory. 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